基于分形的心电信号复杂度及其非线性动力学机制

The complexity of ECG signal based on multifractal theories and its nonlinear dynamical mechanism

体表心电图(electrocardiogram, ECG)信号是典型的非平稳谐和变频信号,属于非线性信号.传统的线性分析方法并不能很好地揭示ECG信号非线性本质.本研究采用多重分形理论,研究了大量样本同步十二导联心电图信号的奇异谱面积,经方差分析(analysis of variance, ANOVA)检验,该参数对所研究人群各导联均统计可分.结果显示,健康年轻人(healthy young, HY)十二导联ECG信号奇异谱面积的算术均值最大、离散度最小,而心梗(myocardial infraction, MI)患者十二导联ECG信号奇异谱面积算术均值最小、离散度最大,其他人群如心肌缺血(ischemia)患者、健康老年人(healthy old, HO)这两个值均处于中等大小水平.表明随着病变程度加深,心脏组织类分形结构受损或者发生结构改变,导致心电系统非线性动力学复杂程度降低,同时增加了心电信号传播的不规则性和各向异性.另外研究发现, ECG信号奇异谱面积在一定程度上反映了人体自主神经控制的强弱.随着年龄增长,奇异谱面积的十二导联均值逐渐减小,提示自主神经的自律控制功能逐渐减弱;ECG信号非线性复杂性下降,由多重分形趋向单重分形,意味着个体适应能力的降低.

The nonlinear dynamical analysis of biomedical signals has always been the research focus in academic fields. It better uncovers the essential rules in life activities than conventional linear and time-frequency analysis methods. Human body surface electrocardiogram(ECG) signal is non-stationary and frequency-varying by nature, which belongs to a typical nonlinear signal. Therefore, traditional linear analysis methods cannot completely disclose its nonlinear nature. The existing nonlinear dynamic tools, such as correlation dimension(D2), Lyapunov exponent,entropy, detrended fluctuation analysis, multifractal singularity spectrum etc., have already been applied to the studies on heart electrical signals, which proved that this signal has definite chaotic characteristic. The aforementioned nonlinear methods perform better in the analysis of deterministic stochastic signals.In our viewpoints, because all the probabilities in the original data set can be exactly expressed by the corresponding points in the multifractal singularity spectrum f(α), the area of the spectrum must comprise the total information of the data. This two-dimensional expression is more accurate than the computation of spectral width Δα in analyzing the heartbeat signal. With regard to ECG time series, the areas of singularity spectrum should include all the information about the heartbeat dynamics. Considering the irregularity and anisotropy of the heartbeat electrical signal propagation, we investigated the arithmetic mean and dispersing degree of the area calculated from synchronous 12-lead ECG signals obtained from a large number of subjects, who were under different physiological and pathological conditions. The 12-lead ECG records were obtained from 12 sensors positioned on body surfaces, including the limb and chest leads. In addition, the ECG signals were in high frequency section(HFECG), whose frequency components were above 100 Hz(approximately 100 Hz–2 kHz). Some early heart diseases can first be reflected by high-frequency ECG signals, which are often associated with sharp notches and slurs in the time domain. Furthermore, we set sampling frequency of HFECG signal to 1 kHz so that all the components below 500 Hz could be analyzed according to the sampling theorem.Thereafter, by the virtue of the multifractal theory, we investigated the arithmetic mean and dispersing degree computed from singularity spectrum area of synchronous 12-lead ECG signals obtained from different crowds of human subjects. Variance analysis tests revealed all 12-lead ECG signals from above cohorts were statistically identifiable using these two indicators. The experimental results suggest that the arithmetic mean of the area of the 12-lead ECG signals was apparently large for healthy young but small for myocardial infarction(MI)sufferers. Besides, the dispersing degree of the area of the 12-lead ECG signals was obviously small for healthy young but large for MI sufferers. For the other cohorts, such as ischemia sufferers and healthy elderly, these two values were of middle magnitudes. This indicates that with deeper lesions, the fractal-like structure of the heartbeat system is damaged or structurally changed, which may lead to decline in the nonlinear complexity of the system and concomitant increase in the irregularity and anisotropic propagation of ECG signal. In addition, we found that the 12-lead mean value of singularity spectrum area of human ECG signals can reflect the self-discipline control status of human autonomic nerve to some degree. This value gradually decreased with aging. These findings suggest that the self-discipline control of the human autonomic nervous system weakens with aging. The nonlinear complexity of ECG signal then descends and tends to turn from multifractality to monofractality, implying weakened human individual adaptabilities. Our studies on the nonlinear dynamical features of heart electrical signals and ECG variations with age, disease, and human autonomic nerve control, demonstrate theoretical and diagnostic significances.